A critical remark on “Fixed point theorems for occasionally weakly compatible mappings”
In the present paper, we show that under contractive conditions, the existence of a common fixed point and occasional weak compatibility are equivalent conditions. We also show that contractive conditions employed by Jungck and Rhoades [Fixed point theorems for occasionally weakly compatible mapping...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2013-10-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X13000400 |
| _version_ | 1819135818423336960 |
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| author | Ravindra K. Bisht R.P. Pant |
| author_facet | Ravindra K. Bisht R.P. Pant |
| author_sort | Ravindra K. Bisht |
| collection | DOAJ |
| description | In the present paper, we show that under contractive conditions, the existence of a common fixed point and occasional weak compatibility are equivalent conditions. We also show that contractive conditions employed by Jungck and Rhoades [Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7(2) (2006) 287–296; Fixed Point Theory 9 (2008) 383–384 (erratum)] do not provide a nontrivial setting for the application of occasional weak compatible mappings. Finally, we improve the results of Jungck and Rhoades by employing a proper setting. |
| first_indexed | 2024-12-22T10:25:08Z |
| format | Article |
| id | doaj.art-d3bcd98ab08848f0bf1fa0fd44f37fe5 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-22T10:25:08Z |
| publishDate | 2013-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-d3bcd98ab08848f0bf1fa0fd44f37fe52022-12-21T18:29:30ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2013-10-0121327327510.1016/j.joems.2013.03.010A critical remark on “Fixed point theorems for occasionally weakly compatible mappings”Ravindra K. Bisht0R.P. Pant1Department of Mathematics–Applied Sciences & Humanities, Bipin Tripahti Kumaon Institute of Technology, Dwarahat, 262 553 Almora, Uttarakhand, IndiaDepartment of Mathematics, D.S.B. Campus, Kumaun University, 263 002 Nainital, Uttarakhand, IndiaIn the present paper, we show that under contractive conditions, the existence of a common fixed point and occasional weak compatibility are equivalent conditions. We also show that contractive conditions employed by Jungck and Rhoades [Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7(2) (2006) 287–296; Fixed Point Theory 9 (2008) 383–384 (erratum)] do not provide a nontrivial setting for the application of occasional weak compatible mappings. Finally, we improve the results of Jungck and Rhoades by employing a proper setting.http://www.sciencedirect.com/science/article/pii/S1110256X13000400Fixed point theoremsOccasionally weakly compatible and (E.A.) property |
| spellingShingle | Ravindra K. Bisht R.P. Pant A critical remark on “Fixed point theorems for occasionally weakly compatible mappings” Journal of the Egyptian Mathematical Society Fixed point theorems Occasionally weakly compatible and (E.A.) property |
| title | A critical remark on “Fixed point theorems for occasionally weakly compatible mappings” |
| title_full | A critical remark on “Fixed point theorems for occasionally weakly compatible mappings” |
| title_fullStr | A critical remark on “Fixed point theorems for occasionally weakly compatible mappings” |
| title_full_unstemmed | A critical remark on “Fixed point theorems for occasionally weakly compatible mappings” |
| title_short | A critical remark on “Fixed point theorems for occasionally weakly compatible mappings” |
| title_sort | critical remark on fixed point theorems for occasionally weakly compatible mappings |
| topic | Fixed point theorems Occasionally weakly compatible and (E.A.) property |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X13000400 |
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